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<FONT color="green">001</FONT>    /*<a name="line.1"></a>
<FONT color="green">002</FONT>     * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
<FONT color="green">003</FONT>     * contributor license agreements.  See the NOTICE file distributed with<a name="line.3"></a>
<FONT color="green">004</FONT>     * this work for additional information regarding copyright ownership.<a name="line.4"></a>
<FONT color="green">005</FONT>     * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
<FONT color="green">006</FONT>     * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
<FONT color="green">007</FONT>     * the License.  You may obtain a copy of the License at<a name="line.7"></a>
<FONT color="green">008</FONT>     *<a name="line.8"></a>
<FONT color="green">009</FONT>     *      http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
<FONT color="green">010</FONT>     *<a name="line.10"></a>
<FONT color="green">011</FONT>     * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
<FONT color="green">012</FONT>     * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
<FONT color="green">013</FONT>     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
<FONT color="green">014</FONT>     * See the License for the specific language governing permissions and<a name="line.14"></a>
<FONT color="green">015</FONT>     * limitations under the License.<a name="line.15"></a>
<FONT color="green">016</FONT>     */<a name="line.16"></a>
<FONT color="green">017</FONT>    package org.apache.commons.math3.optim.nonlinear.vector.jacobian;<a name="line.17"></a>
<FONT color="green">018</FONT>    <a name="line.18"></a>
<FONT color="green">019</FONT>    import org.apache.commons.math3.exception.DimensionMismatchException;<a name="line.19"></a>
<FONT color="green">020</FONT>    import org.apache.commons.math3.exception.TooManyEvaluationsException;<a name="line.20"></a>
<FONT color="green">021</FONT>    import org.apache.commons.math3.linear.ArrayRealVector;<a name="line.21"></a>
<FONT color="green">022</FONT>    import org.apache.commons.math3.linear.RealMatrix;<a name="line.22"></a>
<FONT color="green">023</FONT>    import org.apache.commons.math3.linear.DecompositionSolver;<a name="line.23"></a>
<FONT color="green">024</FONT>    import org.apache.commons.math3.linear.MatrixUtils;<a name="line.24"></a>
<FONT color="green">025</FONT>    import org.apache.commons.math3.linear.QRDecomposition;<a name="line.25"></a>
<FONT color="green">026</FONT>    import org.apache.commons.math3.linear.EigenDecomposition;<a name="line.26"></a>
<FONT color="green">027</FONT>    import org.apache.commons.math3.optim.OptimizationData;<a name="line.27"></a>
<FONT color="green">028</FONT>    import org.apache.commons.math3.optim.ConvergenceChecker;<a name="line.28"></a>
<FONT color="green">029</FONT>    import org.apache.commons.math3.optim.PointVectorValuePair;<a name="line.29"></a>
<FONT color="green">030</FONT>    import org.apache.commons.math3.optim.nonlinear.vector.Weight;<a name="line.30"></a>
<FONT color="green">031</FONT>    import org.apache.commons.math3.optim.nonlinear.vector.JacobianMultivariateVectorOptimizer;<a name="line.31"></a>
<FONT color="green">032</FONT>    import org.apache.commons.math3.util.FastMath;<a name="line.32"></a>
<FONT color="green">033</FONT>    <a name="line.33"></a>
<FONT color="green">034</FONT>    /**<a name="line.34"></a>
<FONT color="green">035</FONT>     * Base class for implementing least-squares optimizers.<a name="line.35"></a>
<FONT color="green">036</FONT>     * It provides methods for error estimation.<a name="line.36"></a>
<FONT color="green">037</FONT>     *<a name="line.37"></a>
<FONT color="green">038</FONT>     * @version $Id$<a name="line.38"></a>
<FONT color="green">039</FONT>     * @since 3.1<a name="line.39"></a>
<FONT color="green">040</FONT>     */<a name="line.40"></a>
<FONT color="green">041</FONT>    public abstract class AbstractLeastSquaresOptimizer<a name="line.41"></a>
<FONT color="green">042</FONT>        extends JacobianMultivariateVectorOptimizer {<a name="line.42"></a>
<FONT color="green">043</FONT>        /** Square-root of the weight matrix. */<a name="line.43"></a>
<FONT color="green">044</FONT>        private RealMatrix weightMatrixSqrt;<a name="line.44"></a>
<FONT color="green">045</FONT>        /** Cost value (square root of the sum of the residuals). */<a name="line.45"></a>
<FONT color="green">046</FONT>        private double cost;<a name="line.46"></a>
<FONT color="green">047</FONT>    <a name="line.47"></a>
<FONT color="green">048</FONT>        /**<a name="line.48"></a>
<FONT color="green">049</FONT>         * @param checker Convergence checker.<a name="line.49"></a>
<FONT color="green">050</FONT>         */<a name="line.50"></a>
<FONT color="green">051</FONT>        protected AbstractLeastSquaresOptimizer(ConvergenceChecker&lt;PointVectorValuePair&gt; checker) {<a name="line.51"></a>
<FONT color="green">052</FONT>            super(checker);<a name="line.52"></a>
<FONT color="green">053</FONT>        }<a name="line.53"></a>
<FONT color="green">054</FONT>    <a name="line.54"></a>
<FONT color="green">055</FONT>        /**<a name="line.55"></a>
<FONT color="green">056</FONT>         * Computes the weighted Jacobian matrix.<a name="line.56"></a>
<FONT color="green">057</FONT>         *<a name="line.57"></a>
<FONT color="green">058</FONT>         * @param params Model parameters at which to compute the Jacobian.<a name="line.58"></a>
<FONT color="green">059</FONT>         * @return the weighted Jacobian: W&lt;sup&gt;1/2&lt;/sup&gt; J.<a name="line.59"></a>
<FONT color="green">060</FONT>         * @throws DimensionMismatchException if the Jacobian dimension does not<a name="line.60"></a>
<FONT color="green">061</FONT>         * match problem dimension.<a name="line.61"></a>
<FONT color="green">062</FONT>         */<a name="line.62"></a>
<FONT color="green">063</FONT>        protected RealMatrix computeWeightedJacobian(double[] params) {<a name="line.63"></a>
<FONT color="green">064</FONT>            return weightMatrixSqrt.multiply(MatrixUtils.createRealMatrix(computeJacobian(params)));<a name="line.64"></a>
<FONT color="green">065</FONT>        }<a name="line.65"></a>
<FONT color="green">066</FONT>    <a name="line.66"></a>
<FONT color="green">067</FONT>        /**<a name="line.67"></a>
<FONT color="green">068</FONT>         * Computes the cost.<a name="line.68"></a>
<FONT color="green">069</FONT>         *<a name="line.69"></a>
<FONT color="green">070</FONT>         * @param residuals Residuals.<a name="line.70"></a>
<FONT color="green">071</FONT>         * @return the cost.<a name="line.71"></a>
<FONT color="green">072</FONT>         * @see #computeResiduals(double[])<a name="line.72"></a>
<FONT color="green">073</FONT>         */<a name="line.73"></a>
<FONT color="green">074</FONT>        protected double computeCost(double[] residuals) {<a name="line.74"></a>
<FONT color="green">075</FONT>            final ArrayRealVector r = new ArrayRealVector(residuals);<a name="line.75"></a>
<FONT color="green">076</FONT>            return FastMath.sqrt(r.dotProduct(getWeight().operate(r)));<a name="line.76"></a>
<FONT color="green">077</FONT>        }<a name="line.77"></a>
<FONT color="green">078</FONT>    <a name="line.78"></a>
<FONT color="green">079</FONT>        /**<a name="line.79"></a>
<FONT color="green">080</FONT>         * Gets the root-mean-square (RMS) value.<a name="line.80"></a>
<FONT color="green">081</FONT>         *<a name="line.81"></a>
<FONT color="green">082</FONT>         * The RMS the root of the arithmetic mean of the square of all weighted<a name="line.82"></a>
<FONT color="green">083</FONT>         * residuals.<a name="line.83"></a>
<FONT color="green">084</FONT>         * This is related to the criterion that is minimized by the optimizer<a name="line.84"></a>
<FONT color="green">085</FONT>         * as follows: If &lt;em&gt;c&lt;/em&gt; if the criterion, and &lt;em&gt;n&lt;/em&gt; is the<a name="line.85"></a>
<FONT color="green">086</FONT>         * number of measurements, then the RMS is &lt;em&gt;sqrt (c/n)&lt;/em&gt;.<a name="line.86"></a>
<FONT color="green">087</FONT>         *<a name="line.87"></a>
<FONT color="green">088</FONT>         * @return the RMS value.<a name="line.88"></a>
<FONT color="green">089</FONT>         */<a name="line.89"></a>
<FONT color="green">090</FONT>        public double getRMS() {<a name="line.90"></a>
<FONT color="green">091</FONT>            return FastMath.sqrt(getChiSquare() / getTargetSize());<a name="line.91"></a>
<FONT color="green">092</FONT>        }<a name="line.92"></a>
<FONT color="green">093</FONT>    <a name="line.93"></a>
<FONT color="green">094</FONT>        /**<a name="line.94"></a>
<FONT color="green">095</FONT>         * Get a Chi-Square-like value assuming the N residuals follow N<a name="line.95"></a>
<FONT color="green">096</FONT>         * distinct normal distributions centered on 0 and whose variances are<a name="line.96"></a>
<FONT color="green">097</FONT>         * the reciprocal of the weights.<a name="line.97"></a>
<FONT color="green">098</FONT>         * @return chi-square value<a name="line.98"></a>
<FONT color="green">099</FONT>         */<a name="line.99"></a>
<FONT color="green">100</FONT>        public double getChiSquare() {<a name="line.100"></a>
<FONT color="green">101</FONT>            return cost * cost;<a name="line.101"></a>
<FONT color="green">102</FONT>        }<a name="line.102"></a>
<FONT color="green">103</FONT>    <a name="line.103"></a>
<FONT color="green">104</FONT>        /**<a name="line.104"></a>
<FONT color="green">105</FONT>         * Gets the square-root of the weight matrix.<a name="line.105"></a>
<FONT color="green">106</FONT>         *<a name="line.106"></a>
<FONT color="green">107</FONT>         * @return the square-root of the weight matrix.<a name="line.107"></a>
<FONT color="green">108</FONT>         */<a name="line.108"></a>
<FONT color="green">109</FONT>        public RealMatrix getWeightSquareRoot() {<a name="line.109"></a>
<FONT color="green">110</FONT>            return weightMatrixSqrt.copy();<a name="line.110"></a>
<FONT color="green">111</FONT>        }<a name="line.111"></a>
<FONT color="green">112</FONT>    <a name="line.112"></a>
<FONT color="green">113</FONT>        /**<a name="line.113"></a>
<FONT color="green">114</FONT>         * Sets the cost.<a name="line.114"></a>
<FONT color="green">115</FONT>         *<a name="line.115"></a>
<FONT color="green">116</FONT>         * @param cost Cost value.<a name="line.116"></a>
<FONT color="green">117</FONT>         */<a name="line.117"></a>
<FONT color="green">118</FONT>        protected void setCost(double cost) {<a name="line.118"></a>
<FONT color="green">119</FONT>            this.cost = cost;<a name="line.119"></a>
<FONT color="green">120</FONT>        }<a name="line.120"></a>
<FONT color="green">121</FONT>    <a name="line.121"></a>
<FONT color="green">122</FONT>        /**<a name="line.122"></a>
<FONT color="green">123</FONT>         * Get the covariance matrix of the optimized parameters.<a name="line.123"></a>
<FONT color="green">124</FONT>         * &lt;br/&gt;<a name="line.124"></a>
<FONT color="green">125</FONT>         * Note that this operation involves the inversion of the<a name="line.125"></a>
<FONT color="green">126</FONT>         * &lt;code&gt;J&lt;sup&gt;T&lt;/sup&gt;J&lt;/code&gt; matrix, where {@code J} is the<a name="line.126"></a>
<FONT color="green">127</FONT>         * Jacobian matrix.<a name="line.127"></a>
<FONT color="green">128</FONT>         * The {@code threshold} parameter is a way for the caller to specify<a name="line.128"></a>
<FONT color="green">129</FONT>         * that the result of this computation should be considered meaningless,<a name="line.129"></a>
<FONT color="green">130</FONT>         * and thus trigger an exception.<a name="line.130"></a>
<FONT color="green">131</FONT>         *<a name="line.131"></a>
<FONT color="green">132</FONT>         * @param params Model parameters.<a name="line.132"></a>
<FONT color="green">133</FONT>         * @param threshold Singularity threshold.<a name="line.133"></a>
<FONT color="green">134</FONT>         * @return the covariance matrix.<a name="line.134"></a>
<FONT color="green">135</FONT>         * @throws org.apache.commons.math3.linear.SingularMatrixException<a name="line.135"></a>
<FONT color="green">136</FONT>         * if the covariance matrix cannot be computed (singular problem).<a name="line.136"></a>
<FONT color="green">137</FONT>         */<a name="line.137"></a>
<FONT color="green">138</FONT>        public double[][] computeCovariances(double[] params,<a name="line.138"></a>
<FONT color="green">139</FONT>                                             double threshold) {<a name="line.139"></a>
<FONT color="green">140</FONT>            // Set up the Jacobian.<a name="line.140"></a>
<FONT color="green">141</FONT>            final RealMatrix j = computeWeightedJacobian(params);<a name="line.141"></a>
<FONT color="green">142</FONT>    <a name="line.142"></a>
<FONT color="green">143</FONT>            // Compute transpose(J)J.<a name="line.143"></a>
<FONT color="green">144</FONT>            final RealMatrix jTj = j.transpose().multiply(j);<a name="line.144"></a>
<FONT color="green">145</FONT>    <a name="line.145"></a>
<FONT color="green">146</FONT>            // Compute the covariances matrix.<a name="line.146"></a>
<FONT color="green">147</FONT>            final DecompositionSolver solver<a name="line.147"></a>
<FONT color="green">148</FONT>                = new QRDecomposition(jTj, threshold).getSolver();<a name="line.148"></a>
<FONT color="green">149</FONT>            return solver.getInverse().getData();<a name="line.149"></a>
<FONT color="green">150</FONT>        }<a name="line.150"></a>
<FONT color="green">151</FONT>    <a name="line.151"></a>
<FONT color="green">152</FONT>        /**<a name="line.152"></a>
<FONT color="green">153</FONT>         * Computes an estimate of the standard deviation of the parameters. The<a name="line.153"></a>
<FONT color="green">154</FONT>         * returned values are the square root of the diagonal coefficients of the<a name="line.154"></a>
<FONT color="green">155</FONT>         * covariance matrix, {@code sd(a[i]) ~= sqrt(C[i][i])}, where {@code a[i]}<a name="line.155"></a>
<FONT color="green">156</FONT>         * is the optimized value of the {@code i}-th parameter, and {@code C} is<a name="line.156"></a>
<FONT color="green">157</FONT>         * the covariance matrix.<a name="line.157"></a>
<FONT color="green">158</FONT>         *<a name="line.158"></a>
<FONT color="green">159</FONT>         * @param params Model parameters.<a name="line.159"></a>
<FONT color="green">160</FONT>         * @param covarianceSingularityThreshold Singularity threshold (see<a name="line.160"></a>
<FONT color="green">161</FONT>         * {@link #computeCovariances(double[],double) computeCovariances}).<a name="line.161"></a>
<FONT color="green">162</FONT>         * @return an estimate of the standard deviation of the optimized parameters<a name="line.162"></a>
<FONT color="green">163</FONT>         * @throws org.apache.commons.math3.linear.SingularMatrixException<a name="line.163"></a>
<FONT color="green">164</FONT>         * if the covariance matrix cannot be computed.<a name="line.164"></a>
<FONT color="green">165</FONT>         */<a name="line.165"></a>
<FONT color="green">166</FONT>        public double[] computeSigma(double[] params,<a name="line.166"></a>
<FONT color="green">167</FONT>                                     double covarianceSingularityThreshold) {<a name="line.167"></a>
<FONT color="green">168</FONT>            final int nC = params.length;<a name="line.168"></a>
<FONT color="green">169</FONT>            final double[] sig = new double[nC];<a name="line.169"></a>
<FONT color="green">170</FONT>            final double[][] cov = computeCovariances(params, covarianceSingularityThreshold);<a name="line.170"></a>
<FONT color="green">171</FONT>            for (int i = 0; i &lt; nC; ++i) {<a name="line.171"></a>
<FONT color="green">172</FONT>                sig[i] = FastMath.sqrt(cov[i][i]);<a name="line.172"></a>
<FONT color="green">173</FONT>            }<a name="line.173"></a>
<FONT color="green">174</FONT>            return sig;<a name="line.174"></a>
<FONT color="green">175</FONT>        }<a name="line.175"></a>
<FONT color="green">176</FONT>    <a name="line.176"></a>
<FONT color="green">177</FONT>        /**<a name="line.177"></a>
<FONT color="green">178</FONT>         * {@inheritDoc}<a name="line.178"></a>
<FONT color="green">179</FONT>         *<a name="line.179"></a>
<FONT color="green">180</FONT>         * @param optData Optimization data. The following data will be looked for:<a name="line.180"></a>
<FONT color="green">181</FONT>         * &lt;ul&gt;<a name="line.181"></a>
<FONT color="green">182</FONT>         *  &lt;li&gt;{@link org.apache.commons.math3.optim.MaxEval}&lt;/li&gt;<a name="line.182"></a>
<FONT color="green">183</FONT>         *  &lt;li&gt;{@link org.apache.commons.math3.optim.InitialGuess}&lt;/li&gt;<a name="line.183"></a>
<FONT color="green">184</FONT>         *  &lt;li&gt;{@link org.apache.commons.math3.optim.SimpleBounds}&lt;/li&gt;<a name="line.184"></a>
<FONT color="green">185</FONT>         *  &lt;li&gt;{@link org.apache.commons.math3.optim.nonlinear.vector.Target}&lt;/li&gt;<a name="line.185"></a>
<FONT color="green">186</FONT>         *  &lt;li&gt;{@link org.apache.commons.math3.optim.nonlinear.vector.Weight}&lt;/li&gt;<a name="line.186"></a>
<FONT color="green">187</FONT>         *  &lt;li&gt;{@link org.apache.commons.math3.optim.nonlinear.vector.ModelFunction}&lt;/li&gt;<a name="line.187"></a>
<FONT color="green">188</FONT>         *  &lt;li&gt;{@link org.apache.commons.math3.optim.nonlinear.vector.ModelFunctionJacobian}&lt;/li&gt;<a name="line.188"></a>
<FONT color="green">189</FONT>         * &lt;/ul&gt;<a name="line.189"></a>
<FONT color="green">190</FONT>         * @return {@inheritDoc}<a name="line.190"></a>
<FONT color="green">191</FONT>         * @throws TooManyEvaluationsException if the maximal number of<a name="line.191"></a>
<FONT color="green">192</FONT>         * evaluations is exceeded.<a name="line.192"></a>
<FONT color="green">193</FONT>         * @throws DimensionMismatchException if the initial guess, target, and weight<a name="line.193"></a>
<FONT color="green">194</FONT>         * arguments have inconsistent dimensions.<a name="line.194"></a>
<FONT color="green">195</FONT>         */<a name="line.195"></a>
<FONT color="green">196</FONT>        @Override<a name="line.196"></a>
<FONT color="green">197</FONT>        public PointVectorValuePair optimize(OptimizationData... optData)<a name="line.197"></a>
<FONT color="green">198</FONT>            throws TooManyEvaluationsException {<a name="line.198"></a>
<FONT color="green">199</FONT>            // Retrieve settings.<a name="line.199"></a>
<FONT color="green">200</FONT>            parseOptimizationData(optData);<a name="line.200"></a>
<FONT color="green">201</FONT>            // Set up base class and perform computation.<a name="line.201"></a>
<FONT color="green">202</FONT>            return super.optimize(optData);<a name="line.202"></a>
<FONT color="green">203</FONT>        }<a name="line.203"></a>
<FONT color="green">204</FONT>    <a name="line.204"></a>
<FONT color="green">205</FONT>        /**<a name="line.205"></a>
<FONT color="green">206</FONT>         * Computes the residuals.<a name="line.206"></a>
<FONT color="green">207</FONT>         * The residual is the difference between the observed (target)<a name="line.207"></a>
<FONT color="green">208</FONT>         * values and the model (objective function) value.<a name="line.208"></a>
<FONT color="green">209</FONT>         * There is one residual for each element of the vector-valued<a name="line.209"></a>
<FONT color="green">210</FONT>         * function.<a name="line.210"></a>
<FONT color="green">211</FONT>         *<a name="line.211"></a>
<FONT color="green">212</FONT>         * @param objectiveValue Value of the the objective function. This is<a name="line.212"></a>
<FONT color="green">213</FONT>         * the value returned from a call to<a name="line.213"></a>
<FONT color="green">214</FONT>         * {@link #computeObjectiveValue(double[]) computeObjectiveValue}<a name="line.214"></a>
<FONT color="green">215</FONT>         * (whose array argument contains the model parameters).<a name="line.215"></a>
<FONT color="green">216</FONT>         * @return the residuals.<a name="line.216"></a>
<FONT color="green">217</FONT>         * @throws DimensionMismatchException if {@code params} has a wrong<a name="line.217"></a>
<FONT color="green">218</FONT>         * length.<a name="line.218"></a>
<FONT color="green">219</FONT>         */<a name="line.219"></a>
<FONT color="green">220</FONT>        protected double[] computeResiduals(double[] objectiveValue) {<a name="line.220"></a>
<FONT color="green">221</FONT>            final double[] target = getTarget();<a name="line.221"></a>
<FONT color="green">222</FONT>            if (objectiveValue.length != target.length) {<a name="line.222"></a>
<FONT color="green">223</FONT>                throw new DimensionMismatchException(target.length,<a name="line.223"></a>
<FONT color="green">224</FONT>                                                     objectiveValue.length);<a name="line.224"></a>
<FONT color="green">225</FONT>            }<a name="line.225"></a>
<FONT color="green">226</FONT>    <a name="line.226"></a>
<FONT color="green">227</FONT>            final double[] residuals = new double[target.length];<a name="line.227"></a>
<FONT color="green">228</FONT>            for (int i = 0; i &lt; target.length; i++) {<a name="line.228"></a>
<FONT color="green">229</FONT>                residuals[i] = target[i] - objectiveValue[i];<a name="line.229"></a>
<FONT color="green">230</FONT>            }<a name="line.230"></a>
<FONT color="green">231</FONT>    <a name="line.231"></a>
<FONT color="green">232</FONT>            return residuals;<a name="line.232"></a>
<FONT color="green">233</FONT>        }<a name="line.233"></a>
<FONT color="green">234</FONT>    <a name="line.234"></a>
<FONT color="green">235</FONT>        /**<a name="line.235"></a>
<FONT color="green">236</FONT>         * Scans the list of (required and optional) optimization data that<a name="line.236"></a>
<FONT color="green">237</FONT>         * characterize the problem.<a name="line.237"></a>
<FONT color="green">238</FONT>         * If the weight matrix is specified, the {@link #weightMatrixSqrt}<a name="line.238"></a>
<FONT color="green">239</FONT>         * field is recomputed.<a name="line.239"></a>
<FONT color="green">240</FONT>         *<a name="line.240"></a>
<FONT color="green">241</FONT>         * @param optData Optimization data. The following data will be looked for:<a name="line.241"></a>
<FONT color="green">242</FONT>         * &lt;ul&gt;<a name="line.242"></a>
<FONT color="green">243</FONT>         *  &lt;li&gt;{@link Weight}&lt;/li&gt;<a name="line.243"></a>
<FONT color="green">244</FONT>         * &lt;/ul&gt;<a name="line.244"></a>
<FONT color="green">245</FONT>         */<a name="line.245"></a>
<FONT color="green">246</FONT>        private void parseOptimizationData(OptimizationData... optData) {<a name="line.246"></a>
<FONT color="green">247</FONT>            // The existing values (as set by the previous call) are reused if<a name="line.247"></a>
<FONT color="green">248</FONT>            // not provided in the argument list.<a name="line.248"></a>
<FONT color="green">249</FONT>            for (OptimizationData data : optData) {<a name="line.249"></a>
<FONT color="green">250</FONT>                if (data instanceof Weight) {<a name="line.250"></a>
<FONT color="green">251</FONT>                    weightMatrixSqrt = squareRoot(((Weight) data).getWeight());<a name="line.251"></a>
<FONT color="green">252</FONT>                    // If more data must be parsed, this statement _must_ be<a name="line.252"></a>
<FONT color="green">253</FONT>                    // changed to "continue".<a name="line.253"></a>
<FONT color="green">254</FONT>                    break;<a name="line.254"></a>
<FONT color="green">255</FONT>                }<a name="line.255"></a>
<FONT color="green">256</FONT>            }<a name="line.256"></a>
<FONT color="green">257</FONT>        }<a name="line.257"></a>
<FONT color="green">258</FONT>    <a name="line.258"></a>
<FONT color="green">259</FONT>        /**<a name="line.259"></a>
<FONT color="green">260</FONT>         * Computes the square-root of the weight matrix.<a name="line.260"></a>
<FONT color="green">261</FONT>         *<a name="line.261"></a>
<FONT color="green">262</FONT>         * @param m Symmetric, positive-definite (weight) matrix.<a name="line.262"></a>
<FONT color="green">263</FONT>         * @return the square-root of the weight matrix.<a name="line.263"></a>
<FONT color="green">264</FONT>         */<a name="line.264"></a>
<FONT color="green">265</FONT>        private RealMatrix squareRoot(RealMatrix m) {<a name="line.265"></a>
<FONT color="green">266</FONT>            final EigenDecomposition dec = new EigenDecomposition(m);<a name="line.266"></a>
<FONT color="green">267</FONT>            return dec.getSquareRoot();<a name="line.267"></a>
<FONT color="green">268</FONT>        }<a name="line.268"></a>
<FONT color="green">269</FONT>    }<a name="line.269"></a>




























































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